I don't think it's as easy as saying this artist or that artist created the modern Santa as such - it was a long progress, with a lot of different hands (some more famous than others) leaving their mark.
Nast probably started the ball rolling with his, although his Santa had a kind of body stocking:
Reginald Birch did one in 1906 that was closer to the modern look
E Boyd Smith got even closer in 1908
Other illustrators such as Leyendecker's 1923 take:
and NC Wyeth's from 1925 refined it:
But Sundblom's 1931 Coke Santa is the
iconic version. Oddly, he never seems to have any teeth in Sundblom's illustrations - probably from drinking too much Coke.